{
  "abstract": "We develop a lattice characterization of fermionic 't Hooft anomalies of finite internal symmetries in one and two spatial dimensions, formulated in terms of obstructions to symmetric short-range-entangled (SRE) states. We consider lattice systems formed by tensor product of onsite fermionic and bosonic local degrees of freedom, and finite internal symmetry given by a central extension $\\mathbb Z_2^F\\to G_f\\to G_b$. We extract a hierarchy of fermionic anomaly indices for a given symmetry operator in both (1+1)D and (2+1)D. In (1+1)D, an exact lattice symmetry is characterized by a pair of cohomological data $(n_2,ν_3)$. For $G_f=G_b\\times\\mathbb Z_2^F$, we further show that a symmetry with trivial lattice anomaly indices $(n_2,ν_3)$ is onsiteable and hence admits a symmetric SRE state, establishing that these indices faithfully detect the lattice anomaly. Comparing with continuum fermionic QFT, we find that exact lattice symmetries do not realize the additional $H^1(BG_b,\\mathbb Z_2)$ anomaly layer in continuum QFT. In particular, for $G_b=\\mathbb Z_2$, exact lattice symmetries realize only the even $\\mathbb Z_4$ subgroup of the continuum $\\mathbb Z_8$ classification. In (2+1)D, we identify three successive anomaly layers of cohomological data $(n_2,n_3,ν_4)$. We show that a nontrivial value of any layer obstructs a symmetric SRE state. For $G_f=G_b\\times\\mathbb Z_2^F$, it also forbids a symmetric invertible state. We also construct a non-onsite $\\mathbb Z_4^F$ lattice symmetry in (2+1)D with nontrivial lattice anomaly index that forbids any symmetric invertible states with $c_-\\in\\mathbb{Z}$, therefore forbids any invertible states compatible with onsite $\\mathbb{Z}_4^F$ symmetry. Our results motivate a systematic study of which continuum anomalies admit exact microscopic lattice realizations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.12455",
  "author_total": 2,
  "authors": [
    {
      "name": "Ameya Chavda"
    },
    {
      "name": "Ryohei Kobayashi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/30161fmdwjyb7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.12455",
  "fulltext_url": null,
  "id": "30161fmdwjyb7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.12455",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Topological Materials and Phenomena"
    ]
  ],
  "openalex": "W7203476694",
  "pdf_url": "https://arxiv.org/pdf/2608.12455",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/30161fmdwjyb7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2608.12455",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.12455"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Fermionic Anomalies of Finite Symmetries on Lattices",
  "title_text": "Fermionic Anomalies of Finite Symmetries on Lattices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/30161fmdwjyb7",
  "venue": "arXiv",
  "versions": []
}